Modeling to characterize fractures network in homogeneous petroleum reservoirs

ABSTRACT

Models of complex reservoir systems including fracture networks and faults are provided from pressure transient test data obtained from a well in a region of interest in the reservoir. An analytic solution methodology is provided to interpret well test data signature from the pressure transient test data based on model data formed of simulated flow geometry and pressure data behavior.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to modeling the structure of subsurface reservoirs, and more particularly to forming models of fracture networks in a reservoir based on pressure transient test measurements obtained from a formation layer of interest in the reservoir.

2. Description of the Related Art

In reservoir engineering, accurate modeling of subsurface reservoirs and formations, and numerical simulation of fluid flow related processes through computer processing, are widely used for accurate oil and gas reservoir management and development plans. Both direct and indirect methods are used to assess the nature of the rock containing hydrocarbon fluids.

Direct methods use direct measuring tools such as well logging tools. However, the ability of such tools to obtain data measurements as a function of depth into the reservoir from the tools is shallow, typically on the order of a few inches. For indirect measurements tools such as pressure gauges are used to record pressure changes due to well rate variations. Indirect measurements involve flowing the well and recording the pressure changes with time. The pressure data obtained are then processed in a number of different ways to describe the reservoir and model the fluid flow processes.

Reservoir modeling is, to a great extent, an art and has its benefits and restraints. There are two main methods to model the reservoirs namely; numerical and analytical. Numerical modeling is flexible, however, it can be inaccurate due to instability of computer processing to solve multiple, multi-variable non-linear differential equations expressing the physical relationships of reservoir rock and fluid phenomena and characteristics. Furthermore, since reservoirs of interest are quite large and there is an increasing need for accuracy, hence, numerical models of a reservoir are organized into a large number of individual cells. The number of cells can be from tens to hundreds of millions for typical reservoirs. Instability in the modeling and the gridding effect make numerical modeling unsuitable to address the more complex cases.

Conversely, analytical methods are exact, accurate, stable solutions and serves as a platform to address more general/complex cases. Moreover, generating Type-Curves for unlimited scenarios is a byproduct of the solution. Although, analytical models are more accurate than numerical models, yet, they are much harder to develop especially with complex geology and well geometries, as the number of variables increase and hence, become hard to solve. Therefore, developers tend to simplify such a complex problem by dividing the problem into segments, replacing the real variables with dimensionless variables and also use mathematical transformations should they need to. This approach results in a set of equations comprising important parameters that are solved analytically or so called semi-analytically.

In current oil production operation ventures, it is becoming increasingly likely to encounter complex geology such as natural and/or man-made fractures. In particular, in transient well test pressure data (derivative plots) from complex fractured carbonate and sandstone reservoirs, a unique flow pattern has been observed indicating complex geology characterized by a fracture flow signature in the flow pattern at early times and a conductive fault indicator in late times. The presence of such complex geology and well geometry in formations of interest is also widely identifiable through the growing number of image and production logs. The identification, characterization and modelling of reservoirs with such pressure signatures have, therefore, become increasingly important. However, so far as is known, there is no analytical solution to interpret such well test data signatures and hence, numerical simulation of the flow has so far been done, which is known to be cumbersome and impractical.

SUMMARY OF THE INVENTION

Briefly, the present invention provides a new and improved computer implemented method of determining a model of a subsurface earth formation, having a well intersecting a complex geological network of a fault and a fracture in the formation, based on a pressure transient test of the formation. The computer implemented method obtains a test measure of bottom-hole pressure and also obtains a test pressure derivative at sampled instants of measurement during a pressure transient test of the formation. An estimated reference type-curve set of a plurality of type-curves of well pressures in the well and pressure derivatives for selected test values of reservoir capacity, fracture conductivity, fault conductivity value and distance from the tested well and the formation capacity are received. A model well pressure of the formation is determined based on the test measure of well pressure and an estimated value of fracture conductivity, fault conductivity, distance and the formation capacity. A model pressure derivative is then determined based on the test measure of well pressure and the estimated values in the formation. A model type-curve is then formed of the determined model well pressure of the formation and the model pressure derivative. The model type-curve of the determined model well pressure of the formation and the model pressure derivative are then determined with the plurality of type-curves of the estimated reference type-curve set. If the model type-curve matches one of the plurality of type-curves of the estimated reference type-curve set within an acceptable limit of accuracy, the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation in addition to its proximity and reservoir capacity of the matched type-curve of the estimated reference type-curve set are stored as models of the fracture conductivity and the fault conductivity of the formation. If not, the estimated values are adjusted, and the steps of determining a model well pressure, determining a model pressure derivative, forming a model type-curve and comparing are repeated based on the adjusted estimated value of fracture conductivity, fault conductivity and its remoteness from the tested well along with the formation capacity.

The present invention also provides a new and improved data processing system for determining a model of a subsurface earth formation, having a well intersecting a complex geological network of a fault and a fracture in the formation, based on a pressure transient test of the formation. The data processing system includes a processor, which obtains a test measure of bottom-hole pressure in the well and also a test pressure derivative at sampled instants of measurement during the pressure transient test of the formation. The processor receives an estimated reference type-curve set of a plurality of type-curves of well pressures in the well and pressure derivatives for selected test values of fracture conductivity fault conductivity in the formation. The processor then determines a model well pressure of the formation based on the test measure of well pressure and an estimated value of fracture conductivity and an estimated value of fault conductivity and its proximity along with the reservoir capacity in the formation, and also determines a model pressure derivative based on the test measure of well pressure and the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation. The processor then forms a model type-curve of the determined model well pressure of the formation and the model pressure derivative. The processor next compares the model type-curve of the determined model well pressure of the formation and the model pressure derivative with the plurality of type-curves of the estimated reference type-curve set. If the model type-curve matches one of the plurality of type-curves of the estimated reference type-curve set within an acceptable limit of accuracy, the processor stores the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation of the matched type-curve of the estimated reference type-curve set as models of the fracture conductivity and the fault conductivity and distance to fault in the formation. If not, the processor adjusts one or all of the estimated value of fracture conductivity, estimated value of fault conductivity and distance to the fault in the formation from the tested well and the quality of formation, and repeats the steps of determining a model well pressure, determining a model pressure derivative, forming a model type-curve and comparing based on the adjusted estimated value of fracture conductivity, fault conductivity and distance of the formation and other values. A memory of the data processing system stores the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation of the matched type-curve of the estimated reference type-curve set as models of the fracture conductivity and the fault conductivity of the formation.

The present invention further provides a new and improved data storage device having stored in a non-transitory computer readable medium computer operable instructions for causing a data processing system to determine a model of a subsurface earth formation, having a well intersecting a complex geological network of a fault and a fracture in the formation, based on a pressure transient test of the formation, the instructions stored in the data storage device causing the data processing system to perform a sequence of processing steps. A test measure of bottom-hole pressure is obtained, and a test pressure derivative is also obtained. An estimated reference type-curve set of a plurality of type-curves of well pressures in the well and pressure derivatives for selected test values of fracture conductivity, fault conductivity and distance with reservoir capacity in the formation are received. A model well pressure of the formation is determined based on the test measure of well pressure and an estimated value of fracture conductivity, fault conductivity, distance and reservoir capacity in the formation. A model pressure derivative is then determined based on the test measure of well pressure and the estimated value of fracture conductivity, the estimated value of fault conductivity and distance with reservoir capacity in the formation. A model type-curve is then formed of the determined model well pressure of the formation and the model pressure derivative based on the determined model well pressure of the formation. The model type-curve of the determined model well pressure of the formation and the model pressure derivative are then determined with the plurality of type-curves of the estimated reference type-curve set. If the model type-curve matches one of the plurality of type-curves of the estimated reference type-curve set within an acceptable limit of accuracy, the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation of the matched type-curve of the estimated reference type-curve set are stored as models of the fracture conductivity and the fault conductivity of the formation. If not, one or both of the estimated value of fracture conductivity, an estimated value of fault conductivity and distance with reservoir capacity in the formation are adjusted, and the steps of determining a model well pressure, determining a model pressure derivative, forming a model type-curve and comparing are repeated based on the adjusted estimated value of fracture conductivity, fault conductivity and distance with reservoir capacity of the formation.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view, taken in cross-section, of a producing fractured well in a reservoir formation in the earth having a geologic fault nearby.

FIG. 2 is a plan view of the flow geometry of the well and reservoir formation of FIG. 1.

FIG. 3 is a functional block diagram of a flow chart of data processing steps for developing type-curves of pressure and pressure derivatives as functions of time for different fracture and fault conductivities according to the present invention.

FIG. 4 is a functional block diagram of a flow chart of data processing steps for modeling to characterize fractures networks according to the present invention.

FIG. 5 is a schematic diagram of a data processing system for modeling to characterize fractures networks according to the present invention.

FIG. 6 is a plot of a type-curve of dimensionless pressure and its log pressure derivative as functions of dimensionless time for a range of different fracture and fault conductivities according to the present invention.

FIG. 7 is a plot of a type-curve of dimensionless log pressure derivative as functions of dimensionless time for a range of different fracture and fault conductivities and reflecting an early fracture linear flow according to the present invention.

FIG. 8 is a plot of a type-curve of dimensionless pressure and its log pressure derivative as functions of dimensionless time obtained according to the present invention for a well intersecting a fracture network as compared to a synthetic numerical model of the same well and fracture network.

FIG. 9 is a plot of a type-curve of dimensionless pressure and its log pressure derivative as functions of dimensionless time obtained according to the present invention for a well intersecting a fracture network as compared to a field example data for such a well.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the drawings, FIGS. 1 and 2 illustrate a reservoir formation layer R of interest in an example subsurface hydrocarbon producing reservoir with complex flow geometry. A hydrocarbon producing well 10 in a well bore 12 has been drilled into and through the reservoir as well as through subsurface formations above the depth of the reservoir. The producing well is located in a fracture or fracture matrix 14 in the layer R. The fracture 14 is one component of the complex flow geometry. As indicated at 16, the fracture 14 has a fracture width w_(f).

A fault indicated schematically at 18 is also present in the layer R composed of Region 1, Region 2, and Region 3 nearby the well 10 and the fracture 14. The fault 18 juxtaposes different geometry across a fault between regions identified as Region 2 and Region 3, which are same quality zones in the reservoir. The fault 18 is another component of the complex flow geometry. As indicated at 20, the fault 18 has a fault width W_(f).

FIG. 2 illustrates schematically the complex flow geometry in the reservoir layer R. The flow domain of the reservoir layer R is composed of three areas: (i) the reservoir layer R with its specific rock and fluid parameters and properties), which defines flow as indicated schematically by arrows 22 into and around the fracture network 14, the fractured well 10 and the nearby fault 18; (ii) the fracture 14 (with its specific fracture properties), which allows fluids to flow as indicated by arrows 24 along and into the fracture 14 and towards the well 10; and (iii) the nearby fault 18 (with its specific properties), which allows fluids to flow as indicated by arrows 26 along, across and towards the fractured well 10. The flow per unit area is defined to be positive from above and negative from below. It should be noted that the present invention provides indications to reservoir engineers and analysts information with regard to the reservoir pressure conditions as functions of both time and space in general, and wellbore pressure conditions with regard to time in particular.

To overcome the aforementioned difficulties, the present invention provides a computer implemented methodology of modeling of subsurface reservoirs and formations, and reservoir simulation of such models. The present invention provides improvements to the existing technological processes of characterizing and modeling of subsurface hydrocarbon reservoirs, where complex flow geometry with fractures and faults are present in order to evaluate their development. The present invention is also potentially capable of improving the functioning of computers in performance of reservoir simulation, by reducing the processing time lost due to instability in the simulator processing of the reservoir model.

Nomenclature

Set forth below are nomenclature and the major working equations of the analytical solution, also interchangeably referred to as the model, which are used in calculating pressures and pressure derivatives. In this model, the well is considered to be producing at a constant rate of g STB/d, while the pressures and pressure derivatives and the crossflow rates are determined for the three regions. The Laplace and Fourier transforms have been performed on the equations governing the two dimensional flow in these three regions. These transformations are with respect to dimensionless time (t), in terms of transform parameters (s) and a space variable (x) in terms of transform parameter (p), respectively. The equations (with the associated boundary conditions) are solved in the Laplace space and inverted numerically using a Gaver-Stehfest numerical inversion, such as that described in Villinger, H., “Solving Cylindrical Geothermal Problems Using Gaver-Stehfest Inverse Laplace Transform,” Geophysics, (1985).

a=Distance from origin, ft

B=Formation volume factor, RB/STB

C=Wellbore storage, bbls/psi

c_(f) Formation compressibility, psi⁻¹

c_(t)=Total compressibility, psi⁻¹

d_(F)=Distance to fault, ft

F_(CDf)=Dimensionless fracture conductivity

F_(CF)=Dimensional fracture conductivity, md-ft

F_(CDF)=Dimensionless fault conductivity

F_(CF)=Dimensional fault conductivity, md-ft

k=Matrix permeability, md

k_(f)=Fracture permeability, md

k_(F)=Fault permeability, md

k_(d)=Dimensionless matrix permeability, md

k_(df)=Dimensionless fracture permeability, md

k_(f)·w_(f)=Fracture conductivity, md-ft

f_(r)=Reference permeability, and

k_(n)=(n) reservoir permeability, md

P_(i)=Initial formation pressure, psi

P₁=Region-1 pressure, psi

P₂=Region-2 pressure, psi

P_(f)=Fracture pressure, psi

P_(wf)=Flowing BHP, psi

P_(d)=dimensionless pressure

P_(d1)=Dimensionless Region-1 pressure

P_(d2)=Dimensionless Region-2 pressure

P_(df)=Dimensionless fracture pressure

P_(dwf)=Dimensionless well flowing pressure

p=Pressure in Laplace domain

p=Pressure in Fourier domain

q=Flow rate at surface, STB/D

r_(w)=Wellbore radius, ft

r=Distance from the center of wellbore, ft

s=Laplace parameter

t_(D)=Dimensionless time

t_(Df)=Fracture dimensionless time

w_(f)=Fracture width, ft

x_(f)=Fracture half-length, ft

x_(d)=Dimensionless x-coordinates

y_(d)=Dimensionless y-coordinates

Δp=Pressure change since start of transient test, psi

Δt=Time elapsed since start of test, hours

η=0.0002637 k/φμct, hydraulic diffusivity, ft²/hr

η_(DF)=Fault hydraulic diffusivity, dimensionless

η_(Df)=Fracture hydraulic diffusivity, dimensionless

η_(D)=Matrix hydraulic diffusivity, dimensionless

μ=Viscosity, cp

φ=Porosity, fraction

ρ=Fourier parameter

Subscripts

C=Conductivity

D=Dimensionless

F=Fault

f=Fracture

w=Wellbore

The formation two dimensional flow illustrated in FIGS. 1 and 2 in the regions of the well bore 10, fracture 14 and fault 18 can be characterized according to the following Equations:

$\begin{matrix} {\mspace{79mu} {{{Region}{\; \;}1\text{:}\mspace{14mu} \frac{\partial^{2}{\overset{\_}{\overset{\_}{p}}}_{D\; 1}}{\partial y_{D}^{2}}} = {\left( {\rho^{2} + \frac{s}{\eta_{D}}} \right){\overset{\_}{\overset{\_}{p}}}_{D\; 1}}}} & \left( {1a} \right) \\ {{{Fracture}\text{:}} - {\rho^{2}{\overset{\_}{\overset{\_}{p}}}_{Df}} + {\frac{k_{D}}{F_{CDf}}\left\lbrack {\frac{\partial{\overset{\_}{\overset{\_}{p}}}_{D\; 2}}{\partial y_{D}}_{y_{D} = 0}{{- \frac{\partial{\overset{\_}{\overset{\_}{p}}}_{D\; 1}}{\partial y_{D}}}_{y_{D} = 0}}} \right\rbrack} + {\quad{\frac{\sqrt{2\pi}}{F_{CDf} \cdot s} = \left( \frac{s \cdot {\overset{\_}{\overset{\_}{p}}}_{Df}}{\eta_{Df}} \right)}}} & \left( {1b} \right) \\ {\mspace{79mu} {{{Region}{\; \;}2\text{:}\mspace{14mu} \frac{\partial^{2}{\overset{\_}{\overset{\_}{p}}}_{D\; 2}}{\partial y_{D}^{2}}} = {\left( {\rho^{2} + \frac{s}{\eta_{D}}} \right){\overset{\_}{\overset{\_}{p}}}_{D\; 2}}}} & \left( {1c} \right) \\ {\mspace{79mu} {{{{Fault}\text{:}} - {\rho^{2}{\overset{\_}{\overset{\_}{p}}}_{DF}} + {\frac{k_{D}}{F_{{CD}_{F}}}\left\lbrack {\frac{\partial{\overset{\_}{\overset{\_}{p}}}_{D\; 3}}{\partial y_{D}} - \frac{\partial{\overset{\_}{\overset{\_}{p}}}_{D\; 2}}{\partial y_{D}}} \right\rbrack}_{y_{D} = d_{F}}} = \left( \frac{s \cdot {\overset{\_}{\overset{\_}{p}}}_{DF}}{\eta_{DF}} \right)}} & \left( {1d} \right) \\ {\mspace{79mu} {{{Region}{\; \;}3\text{:}\mspace{14mu} \frac{\partial^{2}{\overset{\_}{\overset{\_}{p}}}_{D\; 3}}{\partial y_{D}^{2}}} = {\left( {\rho^{2} + \frac{s}{\eta_{D}}} \right){\overset{\_}{\overset{\_}{p}}}_{D\; 3}}}} & \left( {1e} \right) \end{matrix}$

Where the qualities of Region 1, 2 & 3 are identical.

As has been described above, Laplace and Fourier transformations are applied to the five equations above governing the two dimensional flow in these three regions, fracture and fault. These mathematical transformations were with respect to dimensionless time (t_(D)), in terms of transformed parameter (s) and a space variable (x_(d)), in terms of the transformed parameter (φ, respectively. The equations (with the associated boundary conditions) were solved in the Laplace space and inverted numerically. The final equation for the wellbore pressure in Laplace domain is set forth in Equation (2) below:

$\quad\begin{matrix} {{\overset{\_}{p}}_{wD} = {\frac{2}{s} {\int_{0}^{\infty}{{\quad {{\quad\quad}{\quad\quad}}\quad}\ \frac{{1 - \left\lbrack {e^{{- 2}{\sqrt{m} \cdot d_{F}}}\left\lbrack \frac{1 - \frac{k_{D} \cdot \sqrt{\left( {\rho^{2} + \frac{s}{\eta_{D}}} \right)}}{{F_{{CD}_{F}} \cdot \left( {\rho^{2} + \frac{s}{\eta_{DF}}} \right)} + {k_{D} \cdot \sqrt{\left( {\rho^{2} + \frac{s}{\eta_{D}}} \right)}}}}{1 + \frac{k_{D} \cdot \sqrt{\left( {\rho^{2} + \frac{s}{\eta_{D}}} \right)}}{{F_{{CD}_{F}} \cdot \left( {\rho^{2} + \frac{s}{\eta_{DF}}} \right)} + {k_{D} \cdot \sqrt{\left( {\rho^{2} + \frac{s}{\eta_{D}}} \right)}}}} \right\rbrack} \right\rbrack}}{\begin{matrix} {\left\lbrack {{F_{{CD}_{f}} \cdot \left( {\rho^{2} + \frac{s}{\eta_{Df}}} \right)} + {2 \cdot k_{D} \cdot \sqrt{\left( {\rho^{2} + \frac{s}{\eta_{D}}} \right)}}} \right\rbrack +} \\ {\left\lbrack {e^{{- 2}{\sqrt{m} \cdot d_{F}}}\left\lbrack \frac{1 - \frac{k_{D} \cdot \sqrt{\left( {\rho^{2} + \frac{s}{\eta_{D}}} \right)}}{{F_{{CD}_{F}} \cdot \left( {\rho^{2} + \frac{s}{\eta_{DF}}} \right)} + {k_{D} \cdot \sqrt{\left( {\rho^{2} + \frac{s}{\eta_{D}}} \right)}}}}{1 + \frac{k_{D} \cdot \sqrt{\left( {\rho^{2} + \frac{s}{\eta_{D}}} \right)}}{{F_{{CD}_{F}} \cdot \left( {\rho^{2} + \frac{s}{\eta_{DF}}} \right)} + {k_{D} \cdot \sqrt{\left( {\rho^{2} + \frac{s}{\eta_{D}}} \right)}}}} \right\rbrack} \right\rbrack \cdot} \\ \left\lbrack {F_{{CD}_{f}} \cdot \left( {\rho^{2} + \frac{s}{\eta_{Df}}} \right)} \right\rbrack \end{matrix}}d\; \rho}}}} & (2) \end{matrix}$

where: η_(D), η_(Df) and η_(DF) are the dimensionless hydraulic diffusivity of matrices, fracture and fault, respectively, as defined:

$\eta_{Dn} = {{0.000264 \cdot \left( {\frac{\left( {\phi \mspace{11mu} c_{t}\mspace{11mu} \mu} \right)_{n}}{k_{f}} \cdot \frac{k_{rn}}{\left( {\phi \mspace{11mu} c_{t}\mspace{11mu} \mu} \right)}} \right)} = {0.000264 \cdot \left( \frac{\eta}{\eta_{n}} \right)}}$

where:

n=1,2,3,f&F

F_(CDf) is the dimensionless fracture conductivity described by

${F_{CDf} = {{\frac{k_{f}w_{f}}{k\mspace{14mu} r_{w}}\mspace{14mu} {and}\mspace{14mu} F_{CDF}} = \frac{k_{F}w_{F}}{k\mspace{14mu} r_{w}}}},$

the region's reference permeability is: k_(r)=1.0 md, and

$k_{D} = \frac{k}{k_{r}}$

is the matrix dimensionless permeability, and the dimensionless pressure is:

${p_{Df} = \frac{k_{rf} \cdot {h\left\lbrack {p_{i} - p_{f}} \right\rbrack}}{141.2q\; {\beta\mu}}},$

the dimensionless coordinates written as:

$x_{D} = {{\frac{x}{r_{w}}\mspace{14mu} {and}\mspace{14mu} y_{D}} = \frac{y}{r_{w}}}$

with the dimensionless time being expressed as:

$t_{D_{f}} = {\frac{0.000264\mspace{14mu} k_{r}t}{{\phi\mu}\; c_{t}r_{w}^{2}}.}$

Processing Methodology

A comprehensive computer implemented methodology of modeling to characterize fractures network in homogeneous petroleum reservoirs according to the present invention is illustrated schematically in FIGS. 3 and 4. FIG. 3 illustrates a flow chart T setting forth the methodology of the present invention for developing type-curves of pressure and pressure derivatives as functions of time for different fracture and fault conductivities. FIG. 4 illustrates a flow chart F setting forth the methodology of the present invention for modeling to characterize fractures networks.

The flow chart T (FIG. 3) and the flow chart F (FIG. 4) illustrate the structure of the logic of the present invention as embodied in computer program software. Those skilled in this art will appreciate that the flow charts illustrate the structures of computer program code elements including logic circuits on an integrated circuit that function according to this invention. Manifestly, the invention is practiced in its essential embodiment by a machine component that renders the program code elements in a form that instructs a digital processing apparatus (that is, a computer) to perform a sequence of data transformation or processing steps corresponding to those shown.

The flow chart T of FIG. 3 illustrates schematically a preferred sequence of steps of a computer implemented process for developing type-curves of pressure and pressure derivatives as functions of dimensionless time for different fracture and fault conductivities for a subsurface formation or layer of interest.

As shown at step 40, processing according to the present invention begins with data regarding the formation rock, fluid and geometric properties of the layer R and well 10 being stored in memory of a data processing system D (FIG. 5). The data regarding formation rock, fluid and geometric properties are obtained from well logs, core samples, fluid analysis reports, pressure transient tests and other conventional sources of such data. During step 42, a starting value for each of dimensional fracture conductivity F_(Cf) and dimensional fault conductivity F_(CF) are initialized.

During step 44, model values of the pressure derivative are obtained by the data processing system D based on a specified input value of dimensional fracture conductivity F_(Cf) and dimensional fault conductivity F_(CF) and the pressure transient test data obtained for the region of interest. The derivative is calculated using a computer code that multiplies the dimensionless time (t_(D)), in terms of Laplace transform parameter (s), by the change in well pressure with respect to time to produce the well test derivative and plot it in a log-log scale. In step 46, the model values of the pressure derivative for the specified input value of dimensional fracture conductivity F_(Cf) and dimensional fault conductivity F_(CF) during step 44 are stored in memory of the data processing system D, together with the input value of dimensional fracture conductivity F_(Cf) and dimensional fault conductivity F_(CF).

As indicated schematically at step 48, the values of fracture conductivity and fault conductivity are adjusted as required for a range of postulated values deemed likely to be present based on the pressure transient test data, and additional model values of pressure derivative obtained as described above in step 44 and stored in memory of the data processing system D. In this way a set of model values for type-curves are stored in the data processing system D and are available as indicated at step 50 for presentation as output displays from the data processing system D for analysis by reservoir engineers and analysts.

The flow chart F of FIG. 4 illustrates schematically a preferred sequence of steps of a computer implemented process for modeling to characterize fractures networks. As indicated at step 60, a time range is selected from the pressure and time data obtained during pressure transient test of layer R. The model and its structure have been described above in terms of Equation 1 in the Laplace domain. During step 62, model values of present pressure and pressure derivative with time are obtained according to the methodology of flowchart T of FIG. 3 and formatted in a form display in log-log plots, and made available for comparison with actual test data and for output display as diagnostic plots by data processing system D (FIG. 5) in such format. During step 64, the petrophysical and reservoir data of both the well 10, fracture 14 and fault 18 are read in from storage memory for processing in the data processing system D.

During step 66, actual values for well pressure and pressure derivative are obtained according to actual measured well pressure transient tests data according to Equation (1) above in the data processing system D. During step 68, model pressure and derivative plots based on actual pressure transient testing are generated and then made ready to compare with the model pressure and derivative of the data obtained during step 62. The well pressure and pressure derivative values determined during step 68 are also formatted in a form for storage and subsequent display in log-log plots, and are available in that format for output display by data processing system D.

During step 70, the values for well pressure and pressure derivative determined from actual pressure transient test data results during step 66 are compared with the model values of well pressure and pressure derivative in the log-plot format resulting from step 62. This comparison is done by super-imposing of pressure data from the actual pressure transient test data results on the proposed type curve or reservoir model.

Step 72 involves an evaluation of the results of comparison step 72. If the well pressure and pressure derivative values obtained during step 68, which are compared with model values during step 70 indicate that the generated actual values being compared do correspond within a specified acceptable degree to the model data, an acceptable value of well pressure and pressure derivative is indicated.

It is a common practice to leave the criteria of determining the closeness between the generated values form actual pressure transient tests and the model values up to the experience and judgment of the user analyst or engineer. Such a process involves minimizing the standard deviation between the measured pressure and pressure derivatives based on postulated fracture and fault conductivity values and the model pressure and pressure and pressure derivative values to a preset criterion value (for example, 0.1). Once such a preset criterion value is satisfied in step 72, the user is thus satisfied to call the model as the reasonably well matched one for the fracture and fault conductivity values

Then, as indicated at step 74 the fracture and fault parameters indicated by the model are reported as those for the layer being analyzed. During step 76, the fracture and fault parameters are displayed as results from the data processing system D.

If the results of step 72 indicate an unacceptable match between pressure or pressure derivative, or both of them, in the measured data and that of the model values being compared, the value of either or both of the dimensional fracture conductivity F_(Cf) and dimensional fault conductivity F_(CF) are adjusted during step 78. The distance to fault d_(F) and matrix permeability k may also be adjusted during step 78. Processing returns to step 66 for processing of the actual well data based on the adjusted values of fracture and/or fault conductivity. Processing continues for further iterations until during step 72 an acceptable agreement is achieved between the measured data and the model data. This indicates, as noted, that the dimensional fracture conductivity and dimensional fault conductivity values of the current iteration are proper indications of the complex flow geometry.

Data Processing System

As illustrated in FIG. 5, the data processing system D includes a computer 100 having a processor 102 and memory 104 coupled to the processor 102 to store operating instructions, control information and database records therein. The data processing system D may be a multicore processor with nodes such as those from Intel Corporation or Advanced Micro Devices (AMD), an HPC Linux cluster computer or a mainframe computer of any conventional type of suitable processing capacity such as those available from International Business Machines (IBM) of Armonk, N.Y. or other source. The data processing system D may also be a computer of any conventional type of suitable processing capacity, such as a personal computer, laptop computer, or any other suitable processing apparatus. It should thus be understood that a number of commercially available data processing systems and types of computers may be used for this purpose.

The processor 102 is, however, typically in the form of a personal computer having a user interface 106 and an output display 108 for displaying output data or records of processing of force measurements performed according to the present invention. The output display 108 includes components such as a printer and an output display screen capable of providing printed output information or visible displays in the form of graphs, data sheets, graphical images, data plots and the like as output records or images.

The user interface 106 of computer 100 also includes a suitable user input device or input/output control unit 110 to provide a user access to control or access information and database records and operate the computer 100.

Data processing system D further includes a database 114 stored in memory, which may be internal memory 114, or an external, networked, or non-networked memory as indicated at 116 in an associated database server 118. The database 114 also contains various data including the time and pressure data obtained during pressure transient testing of the layer under analysis, as well as the rock, fluid and geometric properties of layer R and well 10, and other formation properties, physical constants, parameters, data measurements identified above with respect to FIGS. 1 and 2 and the Nomenclature table.

The data processing system D includes program code 120 stored in a data storage device, such as memory 104 of the computer 100. The program code 120, according to the present invention is in the form of computer operable instructions causing the data processor 102 to perform the methodology of modeling to characterize fractures network in homogeneous petroleum reservoirs as shown in FIGS. 3 and 4.

It should be noted that program code 120 may be in the form of microcode, programs, routines, or symbolic computer operable languages that provide a specific set of ordered operations that control the functioning of the data processing system D and direct its operation. The instructions of program code 120 may be stored in non-transitory memory 104 of the computer 100, or on computer diskette, magnetic tape, conventional hard disk drive, electronic read-only memory, optical storage device, or other appropriate data storage device having a computer usable medium stored thereon. Program code 120 may also be contained on a data storage device such as server 118 as a non-transitory computer readable medium, as shown.

The processor 102 of the computer 100 accesses the pressure transient testing data and other input data measurements as described above to perform the logic of the present invention, which may be executed by the processor 102 as a series of computer-executable instructions. The stored computer operable instructions cause the data processor computer 100 to develop type-curves of pressure and pressure derivatives as functions of time for different fracture and fault conductivities according to the methodology of FIG. 3 and to develop models to characterize fractures networks according to FIG. 4. Results of such processing are then available on output display 108. FIGS. 6 through 9 are example displays of such results.

Model Behavior

FIG. 6 is a display of a model type-curve set of dimensionless time versus dimensionless pressure and its log-derivative for a selected set of different fracture and fault conductivities which have been determined in a data processing system according to the process of FIG. 3 described above. FIG. 6 shows determined model pressure at 200 from well data and the determined model pressure derivative is shown at 202. Radial flow is indicated at 204 in FIG. 6. Model pressure type-curves for a set of selected values of dimensional fracture conductivity F_(Cf) values of 0.1e1, 1.5e2 and 1.5e4 are shown at 210, 212, and 214, respectively, in FIG. 6. Model pressure derivative type curves for a set of selected values of dimensional fault conductivity F_(CF) values of 1e8, 1e9 and 1e10 are shown at 216, 218, and 220, respectively.

The type-curves displayed in FIG. 6 shows some distinctive features of flow conditions of subsurface wells where complex fracture networks may be occurring. First, fractured well pressure behavior at early times such as at 222, where the type-curve indicates a ¼ slope is of interest. This segment of the type-curves is indicative of a bilinear flow well behavior reflecting two linear flow regimes along and into a fracture such as shown schematically at 14 in FIGS. 1 and 2.

The type-curves of FIG. 6 indicate at 224 well behavior of a radial flow demonstrating transient flow in the matrix around a fracture, such as that shown schematically at 22 in FIGS. 1 and 2. Thirdly, a “down-turn” or dip in the type-curves of FIG. 6, such as that shown at 226 with a negative slope of unit value, which is indicative of the beginning of a conductive fault such as that shown schematically at in FIGS. 1 and 2 with enhancement of rock quality. Further, as shown at 228 in the type-curves of FIG. 6, the subsequent increase or up-turn in FIG. 6 indicates a bilinear flow regime and also indicating the finite nature of fault 18. The type-curves of FIG. 6 further indicate at 204 for subsequent time a radial flow regime of the bounding blocks of Regions 1 and Region 2.

FIG. 7 is a display of a model type-curve set of dimensionless time versus dimensionless pressure log-derivative for a different selected set of different dimensional fracture conductivities F_(Cf) and dimensional fault conductivities F_(CF) which have also been determined in a data processing system according to the process of FIG. 3 described above.

The pressure derivative type-curves of FIG. 7 are for dimensional fracture conductivity F_(d) of 1e3, 1e4, 1e5, and 1e6 as indicated and for dimensional fault conductivity F_(CF) of 1e8, 1e9, and 1e10, as indicated. It is noted that the pressure derivative type-curves of FIG. 7 exhibit at 230 a distinctive feature of an early fracture linear flow regime at very early times until such a fracture linear flow ends as shown schematically at 232, with bilinear flow starting at 234 in the manner also indicated in the type-curves of FIG. 6. The early fracture linear flow feature shown in the type-curves of FIG. 7 reflects the first fluid flow into a well from a fracture alone as shown schematically at 10 and 14, and confirms the stability of the solution even at a very early time. The pressure derivative type-curves of FIG. 7 also indicate at 236 beginning of a conductive fault and at 238, a bilinear flow regime of the type described in FIG. 6.

Synthetic Flow Geometry Network Model

A synthetic numerically-built model of simulated flow geometry with a well intersecting a fracture network, was constructed and the pressure data were generated by a backward modelling of the given well rate, fluid, reservoir, fracture and fault parameters and properties. The pressure data for the simulated flow geometry of the model were then analyzed in a commercial well-test package (i. e. ECRIN of KAPPA Associates). The results obtained for the numerical model are shown at 250 in FIG. 8 for pressure and at 252 for pressure derivative. Processing results obtained according to the methods of FIGS. 3 and 4 indicated a dimensional fracture conductivity F_(Cf) value of 1e5 and a dimensional fault conductivity F_(CF) value of 1e8 as indicated in FIG. 8. The results are plotted in a log-log plot format as shown at 262 for pressure and 264 for pressure derivative in FIG. 8, along with the type-curves as indicated at 250 and 252 from the model data. Initial bi-linear flow is indicated in FIG. 8 at 266 in both the model data and the results according to the present invention, followed by beginning of a conductive fault as shown at 268, with a subsequent increase or up-turn shown at 270 indicating bilinear flow, and followed by radial flow as indicated at 272.

Heavy lines 280 and 282 have been added in FIG. 8 in those portions of the data plots, where substantial conformity exists between the type-curves 250 and 260 and the pressure derivative type-curves 252 and 264 for the fracture conductivity of 1e5, and for a fault conductivity of 1e8. As is evident from FIG. 8, a good agreement between the curves plotted is noted in those areas. Table 1 contains a comparison of the fracture conductivities and other parameter values both for the synthetic flow geometry network model and according to the present invention. The value of the permeability is determined by dividing the flow capacity (kh) by the layer thickness. The flow capacity is an output of the model selected. Again, good agreement between the values is also indicated.

TABLE 1 Comparison Between the Results of a Numerically Based Model and the Present Invention Numerical Model Present Invention x_(f) d_(F) F_(Cf)-F_(CF) k x_(f) d_(F) F_(Cf)-F_(CF) k (ft) (ft) (md ft) (md) (ft) (ft) (md ft) (md) 2.0e5 5.0e3 1.0e5-1.0e8 33 Not 5.0e3 1.0e5-1.0e8 33 Esti- mated

Field Data Well Model

A well model case example form an actual well in a producing field provided a data set for comparison with processing results according to the present invention. The well model corresponds to a vertical well intersecting a fracture network in a tight homogenous reservoir. The case example was to evaluate results according to the present invention in comparison with an existing example of data from an actual well. Pressure transient testing of the actual well has determined the well to exhibit a flow which is dominated by a fracture bi-linear flow regime for both pressure type-curve at 298 and pressure derivative type-curve at 256 in FIG. 9, followed by beginning of a conductive fault in pressure derivative type-curve with a negative half-slope as indicated at 290, followed by an increase at 292 indicating a bi-linear flow regime.

Heavy lines 296 and 298 have been added in FIG. 9 in those portions of the data plots where substantial conformity exists between the type-curves according to the present invention for the determined conductivities and the flow geometry model data curves. As is evident from FIG. 9, a good agreement is noted, indicating the dimensional fracture conductivity of 1e5, and for the dimensional fault conductivity of 4.35e4. Table 2 contains an indication of the fracture conductivities and permeability parameter values obtained according to the present invention both for the flow geometry network and the flow measures model. The calculated parameters are resulting from the model match. As a result of the match these parameters are obtained.

TABLE 2 Results Obtained for the Field Data Set by the Approach of the Present Invention Results x_(f) d_(F) F_(Cf)-F_(CF) k (ft) (ft) (md-ft) (md) Not Estimated 105 1.8e3-4.35e4 1.6

Reservoir Permeability, k_(r)

Dimensional Fracture Conductivity,

F_(Cf) = kf ⋅ wf

Dimensionless Fracture Conductivity,

$F_{CDf} = \frac{k_{f}w_{f}}{k_{r} \cdot r_{w}}$

Distance to. Fault, d_(F)

Dimensional Fault Conductivity, F_(Cf)=k_(F)·k_(wf)

Dimensionless Fault Conductivity,

$F_{CDF} = \frac{k_{F}w_{F}}{k_{r} \cdot r_{w}}$

From the foregoing, it can be seen that the present invention provides a new methodology where pressure transient data is processed so that a complex flowing geometry with flow from fractures and faults is rigorously described based on values of fracture conductivities and fault conductivities which are determined. Thus, the present invention provides models of the complex flow geometry which conforms to both numerical models and actual field data. The present invention provides reliable reservoir models based on the pressure transient testing of a reservoir.

Type-curves such as those shown in FIG. 6 indicate how a complex network of fractures appears when recording pressure transient data from oil and gas wells in a reservoir. Accordingly, data that show similar behavior can be matched using such type-curves. Once the match is obtained, the values of the fracture nature and dimensions can be determined with a high degree of accuracy.

The present invention thus provides accurate semi-analytical solutions for a well intersecting fractures network in homogenous reservoir(s). This is of considerable value in view of increasing activities in production from naturally faulted geological settings and unconventional reservoirs. The developed present invention offers more flexible schemes to easily carry out modelling with increasing certainty and larger positive impact on the management decisions of such reservoirs.

The invention has been sufficiently described so that a person with average knowledge in the field of reservoir modeling and simulation may reproduce and obtain the results mentioned in the invention herein. Nonetheless, any skilled person in the field of technique, subject of the invention herein, may carry out modifications not described in the request herein, to apply these modifications to a determined structure and methodology, or in the use and practice thereof, requires the claimed matter in the following claims; such structures and processes shall be covered within the scope of the invention.

It should be noted and understood that there can be improvements and modifications made of the present invention described in detail above without departing from the spirit or scope of the invention as set forth in the accompanying claims. 

What is claimed is:
 1. A computer implemented method of deter wining a model of a subsurface earth formation, having a well intersecting a complex geological network of a fault and a fracture in the formation, based on a pressure transient test of the formation, the computer implemented method comprising the steps of: obtaining a test measure of bottom hole pressure in the well; obtaining a test pressure derivative of well pressure in the well at sampled instants of measurement during the pressure transient test of the formation; receiving an estimated reference type-curve set of a plurality of type-curves of well pressures in the well and pressure derivatives for selected test values of fracture conductivity and fault conductivity in the formation; determining a model well pressure of the formation based on the test measure of well pressure and an estimated value of fracture conductivity and an estimated value of fault conductivity in the formation; determining a model pressure derivative based on the test measure of well pressure and the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation; forming a model type-curve of the determined model well pressure of the formation and the model pressure derivative based on the determined model well pressure of the formation; comparing the model type-curve of the determined model well pressure of the formation and the model pressure derivative with the plurality of type-curves of the estimated reference type-curve set; and if the model type-curve matches one of the plurality of type-curves of the estimated reference type-curve set within an acceptable limit of accuracy, storing the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation of the matched type-curve of the estimated reference type-curve set as models of the fracture conductivity and the fault conductivity of the formation; and if not, adjusting one or both of the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation; and repeating the steps of determining a model well pressure, determining a model pressure derivative, forming a model type-curve and comparing based on the adjusted estimated value of fracture conductivity and fault conductivity of the formation until an acceptable match is achieved.
 2. The computer implemented method of claim 1, further including the step of forming a measure of the formation permeability based on the stored models of the fracture conductivity and the fault conductivity of the formation.
 3. The computer implemented method of claim 1, further including the step of forming an output display of the stored models of the fracture conductivity and the fault conductivity of the formation.
 4. The computer implemented method of claim 1, further including the step of forming an output display of the stored model of the fracture conductivity as dimensional fracture conductivity of the formation.
 5. The computer implemented method of claim 1, further including the step of forming an output display of the stored model of the fracture conductivity as dimensionless fracture conductivity of the formation.
 6. The computer implemented method of claim 1, further including the step of forming an output display of the stored model of the fault conductivity as dimensional fault conductivity of the formation.
 7. The computer implemented method of claim 1, further including the step of forming an output display of the stored model of the fault conductivity as dimensionless fault conductivity of the formation.
 8. A data processing system for determining a model of a subsurface earth formation, having a well intersecting a complex geological network of a fault and a fracture in the formation, based on a pressure transient test of the formation, the data processing system comprising: a processor performing the steps of: obtaining a test measure of bottom-hole pressure in the well; obtaining a test pressure derivative of well pressure in the well at sampled instants of measurement during the pressure transient test of the formation; receiving an estimated reference type-curve set of a plurality of type-curves of well pressures in the well and pressure derivatives for selected test values of fracture conductivity and fault conductivity in the formation; determining a model well pressure of the formation based on the test measure of well pressure and an estimated value of fracture conductivity and an estimated value of fault conductivity in the formation; determining a model pressure derivative based on the test measure of well pressure and the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation; forming a model type-curve of the determined model well pressure of the formation and the model pressure derivative based on the determined model well pressure of the formation; comparing the model type-curve of the determined model well pressure of the formation and the model pressure derivative with the plurality of type-curves of the estimated reference type-curve set; and if the model type-curve matches one of the plurality of type-curves of the estimated reference type-curve set within an acceptable limit of accuracy, storing the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation of the matched type-curve of the estimated reference type-curve set as models of the fracture conductivity and the fault conductivity of the formation; and if not, adjusting one or both of the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation; and repeating the steps of determining a model well pressure, determining a model pressure derivative, forming a model type-curve and comparing based on the adjusted estimated value of fracture conductivity and fault conductivity of the formation until an acceptable match is achieved; and a memory storing the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation of the matched type-curve of the estimated reference type-curve set as models of the fracture conductivity and the fault conductivity of the formation.
 9. The data processing system of claim 8, further including the processor performing the step of: forming a measure of the formation permeability based on the stored models of the fracture conductivity and the fault conductivity of the formation.
 10. The data processing system of claim 8, further including: an output display forming of the stored models of the fracture conductivity and the fault conductivity of the formation.
 11. The data processing system of claim 8, further including: the output display forming an output record of the stored model of the fracture conductivity as dimensional fracture conductivity of the formation.
 12. The data processing system of claim 8, further including: the output display forming an output record of the stored model of the fracture conductivity as dimensionless fracture conductivity of the formation.
 13. The data processing system of claim 8, further including: the output display forming an output record of the stored model of the fault conductivity as dimensional fault conductivity of the formation.
 14. The data processing system of claim 8, further including: the output display forming an output record of the stored model of the fault conductivity as dimensionless fault conductivity of the formation.
 15. A data storage device having stored in a non-transitory computer readable medium computer operable instructions for causing a data processing system to determine a model of a subsurface earth formation, having a well intersecting a complex geological network of a fault and a fracture in the formation, based on a pressure transient test of the formation, the instructions stored in the data storage device causing the data processing system to perform the following steps: obtaining a test measure of bottom-hole pressure in the well; obtaining a test pressure derivative of well pressure in the well at sampled instants of measurement during the pressure transient test of the formation; receiving an estimated reference type-curve set of a plurality of type-curves of well pressures in the well and pressure derivatives for selected test values of fracture conductivity and fault conductivity in the formation; determining a model well pressure of the formation based on the test measure of well pressure and an estimated value of fracture conductivity and an estimated value of fault conductivity in the formation; determining a model pressure derivative based on the test measure of well pressure and the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation; forming a model type-curve of the determined model well pressure of the formation and the model pressure derivative based on the determined model well pressure of the formation; comparing the model type-curve of the determined model well pressure of the formation and the model pressure derivative with the plurality of type-curves of the estimated reference type-curve set; and if the model type-curve matches one of the plurality of type-curves of the estimated reference type-curve set within an acceptable limit of accuracy, storing the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation of the matched type-curve of the estimated reference type-curve set as models of the fracture conductivity and the fault conductivity of the formation; and if not, adjusting one or both of the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation; and repeating the steps of determining a model well pressure, determining a model pressure derivative, forming a model type-curve and comparing based on the adjusted estimated value of fracture conductivity and fault conductivity of the formation until an acceptable match is achieved.
 16. The data storage device of claim 15, wherein the instructions cause the data processing system to perform the step of: forming a measure of the formation permeability based on the stored models of the fracture conductivity and the fault conductivity of the formation.
 17. The data storage device of claim 15, wherein the instructions cause the data processing system to perform the step of: forming an output display of the stored models of the fracture conductivity and the fault conductivity of the formation.
 18. The data storage device of claim 15, wherein the instructions cause the data processing system to perform the step of: forming an output display of the stored model of the fracture conductivity as dimensional fracture conductivity of the formation.
 19. The data storage device of claim 15, wherein the instructions cause the data processing system to perform the step of: forming an output display of the stored model of the fracture conductivity as dimensionless fracture conductivity of the formation.
 20. The data storage device of claim 15, wherein the instructions cause the data processing system to perform the step of: forming an output display of the stored model of the fault conductivity as dimensional fault conductivity of the formation.
 21. The data storage device of claim 15, wherein the instructions cause the data processing system to perform the step of: forming an output display of the stored model of the fault conductivity as dimensionless fault conductivity of the formation. 